How to find the probability of an outcome - SSAT Middle Level Quantitative
Card 1 of 68
Dave has a sock drawer with 8 blue and 10 black socks.
If Dave pulls out one black sock, what is the probability that the next sock he pulls out of the drawer is also black?
Dave has a sock drawer with 8 blue and 10 black socks.
If Dave pulls out one black sock, what is the probability that the next sock he pulls out of the drawer is also black?
Tap to reveal answer
Since the first sock that Dave pulls out is black, there are 17 remaining socks in the drawer, 8 blue and 9 black. The probability that Dave will choose another black is sock is therefore 9 out of 17.
Since the first sock that Dave pulls out is black, there are 17 remaining socks in the drawer, 8 blue and 9 black. The probability that Dave will choose another black is sock is therefore 9 out of 17.
← Didn't Know|Knew It →
All of the clubs are removed from a standard fifty-two-card deck. Two cards are then dealt without replacement. What is the probability that both cards will be red?
All of the clubs are removed from a standard fifty-two-card deck. Two cards are then dealt without replacement. What is the probability that both cards will be red?
Tap to reveal answer
Wihtout the clubs, the deck comprises 39 cards, 26 of which are red.
The probability that the first card will be red will be 
. The probability that the second will then also be red will be 
. Multiply the probabilities, and result is 
Wihtout the clubs, the deck comprises 39 cards, 26 of which are red.
The probability that the first card will be red will be
← Didn't Know|Knew It →
A pair of fair dice are rolled. What is the probability that the sum will be a multiple of 4?
A pair of fair dice are rolled. What is the probability that the sum will be a multiple of 4?
Tap to reveal answer
There are three possible multiples of 4 that can come out: 4, 8, and 12. There are 36 equally probable outcomes; the following will result in a multiple of 4:
These are 9 outcomes out of 36, making the probability 
There are three possible multiples of 4 that can come out: 4, 8, and 12. There are 36 equally probable outcomes; the following will result in a multiple of 4:
These are 9 outcomes out of 36, making the probability
← Didn't Know|Knew It →
A pair of fair dice are rolled. What is the probability that the sum will be a multiple of 3?
A pair of fair dice are rolled. What is the probability that the sum will be a multiple of 3?
Tap to reveal answer
There are four possible multiples of 3 that can come out: 3,6,9, and 12. There are 36 equally probable outcomes; the following will result in a multiple of 3:
These are 12 outcomes out of 36, making the probability 
There are four possible multiples of 3 that can come out: 3,6,9, and 12. There are 36 equally probable outcomes; the following will result in a multiple of 3:
These are 12 outcomes out of 36, making the probability
← Didn't Know|Knew It →
Some balls are placed in a hat - ten red, four blue, six yellow. What is the probability that a randomly drawn ball will not be blue?
Some balls are placed in a hat - ten red, four blue, six yellow. What is the probability that a randomly drawn ball will not be blue?
Tap to reveal answer
There are 20 balls in the hat. All but four - that is, sixteen - are blue, so the probability of a draw resulting in a non-blue ball is 
There are 20 balls in the hat. All but four - that is, sixteen - are blue, so the probability of a draw resulting in a non-blue ball is
← Didn't Know|Knew It →
The red jacks are removed from a standard deck of fifty-two cards. What is the probability that a card randomly drawn from that modified deck will be black?
The red jacks are removed from a standard deck of fifty-two cards. What is the probability that a card randomly drawn from that modified deck will be black?
Tap to reveal answer
The removal of two red jacks - and no black cards - results in there being fifty cards, twenty-six of them black. Therefore, the probability of a randomly drawn card being black is 
.
The removal of two red jacks - and no black cards - results in there being fifty cards, twenty-six of them black. Therefore, the probability of a randomly drawn card being black is
← Didn't Know|Knew It →
A standard deck of cards is modified by adding the red threes from another deck. What is the probability that a card randomly drawn from that modified deck will be a red card?
A standard deck of cards is modified by adding the red threes from another deck. What is the probability that a card randomly drawn from that modified deck will be a red card?
Tap to reveal answer
The addition of two red threes from another deck results in the deck comprising fifty-four cards, twenty-eight of which are red. Therefore, the probability of a randomly drawn card being red is
The addition of two red threes from another deck results in the deck comprising fifty-four cards, twenty-eight of which are red. Therefore, the probability of a randomly drawn card being red is
← Didn't Know|Knew It →
A standard deck of cards is modified by adding the red queens from another deck. What is the probability that a card randomly drawn from that modified deck will be a face card (jack, queen, king)?
A standard deck of cards is modified by adding the red queens from another deck. What is the probability that a card randomly drawn from that modified deck will be a face card (jack, queen, king)?
Tap to reveal answer
There are four cards of each rank in a standard deck; since three ranks - jacks, queens, kings - are considered face cards, this makes twelve face cards out of the fifty-two. But two more face cards - two red queens - have been introduced, so now there are fourteen face cards out of fifty-four. This makes the probability of a randomly drawn card being a face card
There are four cards of each rank in a standard deck; since three ranks - jacks, queens, kings - are considered face cards, this makes twelve face cards out of the fifty-two. But two more face cards - two red queens - have been introduced, so now there are fourteen face cards out of fifty-four. This makes the probability of a randomly drawn card being a face card
← Didn't Know|Knew It →
In a bag of marbles, there are 
blue marbles, 
red marbles, and 
green marbles. What is the probability of drawing two blue marbles in a row?
In a bag of marbles, there are
Tap to reveal answer
The probability of drawing a blue marble on the first try is 
, since there are 
blue marbles out of a total of 
marbles. The probability of drawing a second blue marble is 
, since now there are 
blue marbles remaining out of a total of 
remaining marbles. The probability of drawing two blue marbles in a row is the product of the individual probabilities: 
.
The probability of drawing a blue marble on the first try is
← Didn't Know|Knew It →
If Mark flips a coin and then rolls a die, what are the odds that the coin will be heads and that the die will land on a multiple of 3?
If Mark flips a coin and then rolls a die, what are the odds that the coin will be heads and that the die will land on a multiple of 3?
Tap to reveal answer
If Mark flips a coin, the chance that it will land on heads is 
. On a die, there are 2 out of 6 numbers that are a multiple of 3 (3 and 6); therefore, there is a 
chance that the dice will be a multiple of 3.
The probability that the coin will land on heads and that the dice will be a multiple of 3 is:
If Mark flips a coin, the chance that it will land on heads is
The probability that the coin will land on heads and that the dice will be a multiple of 3 is:
← Didn't Know|Knew It →
Lisa and Fred were flipping a quarter and recording whether it was heads or tails. What is the probability they flip a quarter and it lands on heads, heads, tails, heads, tails? (H,H,T,H,T)
Lisa and Fred were flipping a quarter and recording whether it was heads or tails. What is the probability they flip a quarter and it lands on heads, heads, tails, heads, tails? (H,H,T,H,T)
Tap to reveal answer
There are two possibilities every time you flip a coin and only one outcome. Therefore the probability for flipping either heads or tails each time is 
. When you have multiple trials in a row you multiply the probabilities of each outcome by each other.
There are two possibilities every time you flip a coin and only one outcome. Therefore the probability for flipping either heads or tails each time is
← Didn't Know|Knew It →
A large box contains some balls, each of which is marked with a number; one ball is marked with a "1", two balls are marked with a "2". and so forth up to ten balls with a "10". A blank ball is also included.
Give the probability that a ball drawn at random will NOT be an odd-numbered ball.
A large box contains some balls, each of which is marked with a number; one ball is marked with a "1", two balls are marked with a "2". and so forth up to ten balls with a "10". A blank ball is also included.
Give the probability that a ball drawn at random will NOT be an odd-numbered ball.
Tap to reveal answer
The number of balls in the box is
;
The number of odd-numbered balls is
.
Therefore, there are 
balls that are not marked with an odd number, making the probability that one of these will be drawn 
.
The number of balls in the box is
The number of odd-numbered balls is
Therefore, there are
← Didn't Know|Knew It →
A large box contains some balls, each marked with a whole number from "1" to "10". Each odd number is represented by one ball, which is red; each even number is represented by two balls, one red and one green. Five blank yellow balls are then put in the box.
Give the probability that a randomly-drawn ball will be green.
A large box contains some balls, each marked with a whole number from "1" to "10". Each odd number is represented by one ball, which is red; each even number is represented by two balls, one red and one green. Five blank yellow balls are then put in the box.
Give the probability that a randomly-drawn ball will be green.
Tap to reveal answer
Each whole number from one to ten will be represented by a red ball, for a total of ten balls; each even number will be represented by a green ball, for a total of five balls; there will also be five unmarked yellow balls. The number of balls in the box will be 
, 5 of which are green, making the probability of a random draw resulting in a green ball
.
Each whole number from one to ten will be represented by a red ball, for a total of ten balls; each even number will be represented by a green ball, for a total of five balls; there will also be five unmarked yellow balls. The number of balls in the box will be
← Didn't Know|Knew It →
A large box contains some balls, each of which is marked with a number; one ball is marked with a "1", two balls are marked with a "2". and so forth up to ten balls with a "10". Two blank balls are also included.
Give the probability that a ball drawn at random will be an even-numbered ball.
A large box contains some balls, each of which is marked with a number; one ball is marked with a "1", two balls are marked with a "2". and so forth up to ten balls with a "10". Two blank balls are also included.
Give the probability that a ball drawn at random will be an even-numbered ball.
Tap to reveal answer
The number of balls in the box is
.
The number of balls with even numbers is
.
Therefore, if a ball is drawn at random, the probability that an even-numbered ball will be selected is
The number of balls in the box is
The number of balls with even numbers is
Therefore, if a ball is drawn at random, the probability that an even-numbered ball will be selected is
← Didn't Know|Knew It →
A large box contains some balls, each of which is marked with a letter of the alphabet. Each vowel is represented by three balls, one red and two blue; each consonant is represented by one ball, which is red. Give the probability that a randomly drawn ball will be blue.
Note: For purposes of this question, "Y" is considered a consonant.
A large box contains some balls, each of which is marked with a letter of the alphabet. Each vowel is represented by three balls, one red and two blue; each consonant is represented by one ball, which is red. Give the probability that a randomly drawn ball will be blue.
Note: For purposes of this question, "Y" is considered a consonant.
Tap to reveal answer
Each of the 26 letters is represented by one red ball; in addition, each of the five vowels is represented by two blue balls for a total of 
blue balls. The total number of balls is
.
The probability that a random draw will result in a blue ball being selected is
.
Each of the 26 letters is represented by one red ball; in addition, each of the five vowels is represented by two blue balls for a total of
The probability that a random draw will result in a blue ball being selected is
← Didn't Know|Knew It →
Find the probability of drawing a 5 from a deck of cards.
Find the probability of drawing a 5 from a deck of cards.
Tap to reveal answer
To find the probability of an event, we will use the following formula:
Now, we will calculate the following:
because there are 4 different ways we can draw a 5 from a deck of cards:
- 5 of hearts
- 5 of diamonds
- 5 of spades
- 5 of clubs
Now, we will calculate the following:
because there are 52 different cards we could potentially draw from a deck.
So, we will substitute. We get
Therefore, the probability of drawing a 5 from a deck of cards is 
.
To find the probability of an event, we will use the following formula:
Now, we will calculate the following:
because there are 4 different ways we can draw a 5 from a deck of cards:
- 5 of hearts
- 5 of diamonds
- 5 of spades
- 5 of clubs
Now, we will calculate the following:
because there are 52 different cards we could potentially draw from a deck.
So, we will substitute. We get
Therefore, the probability of drawing a 5 from a deck of cards is
← Didn't Know|Knew It →
A classroom contains the following:
- 14 girls
- 17 boys
Find the probability the teacher calls on a boy.
A classroom contains the following:
- 14 girls
- 17 boys
Find the probability the teacher calls on a boy.
Tap to reveal answer
To find the probability of an event, we will use the following formula:
Now, given the event of calling on a boy, we can calculate:
because there are 17 boys in the classroom who can be called on.
We can also calculate the following:
because there are 31 total students (14 girls + 17 boys = 31 students) who could potentially be called on.
Now, we can substitute. We get
Therefore, the probability of the teacher calling on a boy is 
.
To find the probability of an event, we will use the following formula:
Now, given the event of calling on a boy, we can calculate:
because there are 17 boys in the classroom who can be called on.
We can also calculate the following:
because there are 31 total students (14 girls + 17 boys = 31 students) who could potentially be called on.
Now, we can substitute. We get
Therefore, the probability of the teacher calling on a boy is
← Didn't Know|Knew It →
Dave has a sock drawer with 8 blue and 10 black socks.
If Dave pulls out one black sock, what is the probability that the next sock he pulls out of the drawer is also black?
Dave has a sock drawer with 8 blue and 10 black socks.
If Dave pulls out one black sock, what is the probability that the next sock he pulls out of the drawer is also black?
Tap to reveal answer
Since the first sock that Dave pulls out is black, there are 17 remaining socks in the drawer, 8 blue and 9 black. The probability that Dave will choose another black is sock is therefore 9 out of 17.
Since the first sock that Dave pulls out is black, there are 17 remaining socks in the drawer, 8 blue and 9 black. The probability that Dave will choose another black is sock is therefore 9 out of 17.
← Didn't Know|Knew It →
All of the clubs are removed from a standard fifty-two-card deck. Two cards are then dealt without replacement. What is the probability that both cards will be red?
All of the clubs are removed from a standard fifty-two-card deck. Two cards are then dealt without replacement. What is the probability that both cards will be red?
Tap to reveal answer
Wihtout the clubs, the deck comprises 39 cards, 26 of which are red.
The probability that the first card will be red will be . The probability that the second will then also be red will be . Multiply the probabilities, and result is
Wihtout the clubs, the deck comprises 39 cards, 26 of which are red.
The probability that the first card will be red will be
← Didn't Know|Knew It →
A pair of fair dice are rolled. What is the probability that the sum will be a multiple of 4?
A pair of fair dice are rolled. What is the probability that the sum will be a multiple of 4?
Tap to reveal answer
There are three possible multiples of 4 that can come out: 4, 8, and 12. There are 36 equally probable outcomes; the following will result in a multiple of 4:
These are 9 outcomes out of 36, making the probability
There are three possible multiples of 4 that can come out: 4, 8, and 12. There are 36 equally probable outcomes; the following will result in a multiple of 4:
These are 9 outcomes out of 36, making the probability
← Didn't Know|Knew It →